LLMs can execute every step of chain-of-thought reasoning correctly and still produce wrong final answers. We introduce the Novel Operator Test, a benchmark that separates operator logic from operator name, enabling rigorous distinction between genuine reasoning and pattern retrieval. By evaluating Boolean operators under unfamiliar names across depths 1-10 on five models (up to 8,100 problems each), we demonstrate a reasoning-output dissociation that existing benchmarks cannot detect. At Claude Sonnet 4's depth 7, all 31 errors have verifiably correct reasoning yet wrong declared answers; 17/19 errors in mixed-operator chains exhibit the same pattern. The benchmark reveals two failure types: strategy failures at depth 2, where models attempt terse retrieval (+62pp from scaffolding), and content failures at depth 7, where models reason fully but err systematically (+8-30pp, 0/300 errors post-intervention). A Trojan operator (XOR's truth table under a novel name) confirms name alone does not gate reasoning (p >= 0.49), while Llama's novelty gap widens to 28pp at depth 8-9 with the Trojan at 92-100%, isolating genuine difficulty with novel logic from name unfamiliarity.
Figures & tables
Group
Name
TT
TF
FT
FF
Sym
#T
A (Standard)
AND
T
F
F
F
Y
1
OR
T
T
T
F
Y
3
XOR
F
T
T
F
Y
2
IF-THEN
T
F
T
T
N
3
B (Novel)
BLIF
F
T
F
F
N
1
TARN
F
F
F
T
Y
1
Table 1: Truth tables for all nine operators. Group B operators use novel names. ZENT (Group C) is XOR’s truth table under a novel name, serving as the Trojan control.
Accuracy (%)
Novelty Gap (A − B, pp)
Model
Group
d=1
d=2
d=3
d=4
d=5
d=2
d=3
d=4
d=5
GPT-4o
A (Std)
100
81.0
98.0
97.5
99.5
B (Novel)
100
69.0
99.0
99.5
99.5
12.0
− 1.0
− 2.0
0
C (Trojan)
100
82.0
98.0
100
100
Claude Sonnet 4
A (Std)
100
95.0
92.5
96.5
97.5
B (Novel)
100
93.0
94.0
94.0
98.5
2.0
− 1.5
2.5
− 1.0
Table 2: Accuracy (%) by operator group and chain depth. GPT-4o, Claude Sonnet 4, and QwQ-32B show no meaningful novelty gap at depth 5 ( ∣ gap ∣≤ 6pp). Llama 3.1 70B shows an 11pp gap at depth 5, concentrated on structurally complex novel operators. n=50 instances per cell.
Figure 1: Accuracy by operator group and chain depth (1–5) across five models. The depth-4 data point fills the recovery trajectory between the depth-2 dip and depth-5 ceiling. Llama shows a notable non-monotonic dip at depth 4 (91% Group A), driven by IF-THEN (68%). All conditions use n=50 instances; shaded regions show 95% binomial CIs.
d=1
d=2
d=3
d=4
d=5
Model
XOR
ZENT
XOR
ZENT
XOR
ZENT
XOR
ZENT
XOR
ZENT
p
GPT-4o
100
100
62
82
92
98
90
100
98 ± 4
100 ± 0
1.0
Claude Sonnet 4
100
100
98
100
86
94
100
94
100 ± 0
96 ± 5
0.49
Llama 3.1 70B
100
100
100
88
100
92
96
96
98 ± 4
96 ± 5
1.0
o3-mini
100
100
100
100
100
100
100
100
100 ± 0
98 ± 4
1.0
QwQ-32B
100
96
98
74
100
82
92
100
100 ± 0
100 ± 0
1.0
Table 3: XOR vs. ZENT accuracy (%) by depth ( n=50 per cell). No model shows a significant name effect at depth 5 (Fisher’s exact p≥0.49 ). 95% binomial CIs shown for depth 5; Fisher’s p in rightmost column.
Figure 2: GPT-4o response length and accuracy by chain depth for selected operators. (a) AND stays at 1 token across all depths (pure retrieval); TARN and DREM jump from < 20 tokens at depth 2 to 300+ tokens at depth 3, marking the transition from retrieval to chain-of-thought reasoning. (b) Accuracy dips at depth 2 (the transition point) and recovers at depth 3+ once models adopt explicit reasoning.
Group A (Std)
Group B (Novel)
Group C (Trojan)
Model
Tokens
Acc
Tokens
Acc
Tokens
Acc
GPT-4o
141 ± 181
99.5%
343 ± 67
99.5%
357 ± 35
100%
Claude Sonnet 4
199 ± 54
97.5%
272 ± 15
98.5%
279 ± 16
96%
Llama 3.1 70B
103 ± 180
98.5%
124 ± 168
87.5%
241 ± 117
96%
o3-mini
227 ± 176
100%
630 ± 266
100%
375 ± 118
98%
Table 4: Mean response length (completion tokens ± std. dev.) at depth 5 by operator group ( n=200 for A/B, n=50 for C). GPT-4o’s high Group A variance reflects the bimodal distribution: AND/OR produce 1 token while XOR/IF-THEN produce ∼ 300.
Figure 3: Mean completion tokens at depth 5 by operator group across four of five models (QwQ-32B excluded; response length data not collected). GPT-4o shows the starkest divergence between standard (141 tokens) and novel (343 tokens) groups. Error bars show 95% CIs.
Depth 2
Depth 3
Depth 5
Model
BLIF
TARN
QUEX
DREM
BLIF
TARN
QUEX
DREM
BLIF
TARN
QUEX
DREM
GPT-4o
+10
+62
+6
+26
0
0
0
0
0
0
0
0
Claude Sonnet 4
0
0
0
+30
0
+14
+8
+12
0
0
+4
+12
Llama 3.1 70B
+10
+6
+22
+10
0
+12
+10
+16
+22
+2
+16
+16
Table 5: ETT improvement (pp) on Group B operators ( n=50 per cell). ETT has its largest effect at depth 2, where it bridges the reasoning mode transition (Section 4.3 ). At depths 3–5, ETT helps Llama and Claude but has no effect on GPT-4o (already at ceiling). The ETT experiment uses paired within-experiment baselines with separate variable assignments (seed 44) from the core experiment (seed 42).
IF-THEN
ZENT
TARN
DREM
BLIF
XOR
Baseline (%)
70
82
88
92
100
100
ETT (%)
100
100
100
100
100
100
Δ (pp)
+30
+18
+12
+8
0
0
Fisher’s p
<0.0001
0.003
0.027
0.12
—
—
Baseline errors
15
9
6
4
0
0
on GT=True
15
9
6
4
—
—
Table 6: ETT improvement at depth 7 for Claude Sonnet 4 ( n=50 per cell, seed 142). ETT achieves 100% on all operators. The four operators with baseline errors show +8 to +30pp improvement; controls (BLIF, XOR) are unaffected. All 34 baseline errors answer False on True-ground-truth instances. Note: the deep experiment (Section 4.7 , different seed) produces 31 errors with the same directional pattern.
Model
Group
d=6
d=7
d=8
d=9
d=10
GPT-4o
A (Std)
99.5
100
99.0
100
100
B (Novel)
99.0
100
99.5
99.0
99.0
C (Trojan)
100
100
98.0
100
100
Claude Sonnet 4
A (Std)
99.5
96.0
97.5
99.0
99.5
B (Novel)
94.5
93.5
100
99.5
99.0
C (Trojan)
96.0
80.0
100
100
100
Table 7: Group-level accuracy (%) at depths 6–10 ( n=200 per group cell, n=50 for Trojan). GPT-4o and o3-mini maintain near-perfect accuracy. Claude shows a depth-7 dip with recovery. Llama’s novelty gap widens from 11pp at depth 5 to 28pp at depth 8–9. QwQ-32B tested at d=7 and d=10 only (—); its novelty gap vanishes by d=10.
Figure 4: Two failure modes in LLM logical reasoning. (a) Claude Sonnet 4 accuracy across depths 1–10 by operator group, showing the depth-7 dip with full recovery by depth 8. (b) Strategy failures (GPT-4o d=2, blue squares): low token counts, low accuracy; models attempt retrieval over chain-of-thought. Content failures (Claude d=7, orange diamonds): high token counts ( ∼ 350), moderate accuracy; full reasoning produces wrong answers. (c) Error directionality at Claude’s depth 7: all 31 errors (red) occur on True-ground-truth instances; zero errors on False-ground-truth instances. BLIF and XOR (100% accuracy) serve as controls.
Appendix figures & tables4 assets
Supplementary material from the paper’s appendix.
Appendix
Depth 1
Depth 2
Model
Table
Code
NL
Table
Code
NL
GPT-4o
100
72
89.5
72.5
93.5
76
Claude Sonnet 4
100
100
100
92.5
100
90.5
Llama 3.1 70B
100
88
100
86.5
98
98.5
Appendix
Table 8: Accuracy (%) by representation format for Group B operators ( n=200 per cell, aggregated across 4 operators). Code format matches or exceeds truth tables at depth 2 for all models.
Grp
Operator
Sym
#T
GPT-4o
Claude
Llama
o3-mini
QwQ
A
AND
Y
1
100
100
100
100
100
OR
Y
3
100
100
100
100
100
XOR
Y
2
98
100
98
100
100
IF-THEN
N
3
100
90
96
100
100
B
BLIF
N
1
100
100
94
100
100
TARN
Y
1
98
98
92
100
98
Appendix
Table 9: Accuracy (%) per operator at depth 5 ( n=50 per cell). GPT-4o, Claude, and o3-mini achieve ≥ 90% on all operators. Llama shows difficulty on QUEX (78%) and DREM (86%); QwQ-32B shows difficulty specifically on DREM (78%).
Group
Operator
d=1
d=2
d=3
d=4
d=5
d=2 tokens
A
AND
100
100
100
100
100
1
OR
100
100
100
100
100
1
XOR
100
62
92
90
98
1
IF-THEN
100
62
100
100
100
1
B
BLIF
100
96
100
100
100
1
TARN
100
36
98
100
98
5
Appendix
Table 10: Full per-operator accuracy (%) across all depths for GPT-4o. Non-monotonic depth-2 dip and mean response tokens at depth 2 illustrate the reasoning mode transition. Depth 4 fills the recovery trajectory between depth 3 and 5.
Accuracy (%)
Mean tokens
Operator
Depth
Standard
Show-work
Standard
Show-work
AND
2
100
100
1
361
AND
5
100
100
1
770
OR
2
100
100
1
343
OR
5
100
100
1
749
BLIF
2
87
100
1
475
Appendix
Table 11: Standard vs. “show your work” prompts for GPT-4o ( n=30 per cell). Show-work prompt forces verbose reasoning (342–770 tokens for AND/OR) and eliminates depth-2 strategy failures (TARN: 33% → 100%).
Chain-of-thought traces from large reasoning models can span tens of thousands of tokens, yet we lack a vocabulary for describing their internal structure. Previous methods developed to analyze chain-of-thought traces are either too rigid or not expressive enough, failing to capture features across domains and models. To remedy this, we develop ReasonOps, an unsupervised, expressive method for annotating chain-of-thought traces, providing succinct universal operators. Using ReasonOps, we analyze 44,662 traces from 12 thinking LLMs spanning 6 families across 8 reasoning benchmarks and discover that they share a common compositional structure: 7 recurring reasoning operators -- discourse-level moves such as backtracking, inferring, and hypothesizing -- that emerge from unsupervised clustering of sentence-initial 3-token pivots. These operators appear across every model family and benchmark domain, confirmed by three independent LLM judges who classify held-out samples at 70 -76% accuracy. We analyze the structure of operators on easy vs. hard problems, revealing that reflective operators are more helpful on hard problems and harm performance on easy problems. Operator sequences are highly model-identifying: a classifier trained on operator distributions alone recovers the source model with macro-AUC, revealing that each model family has a distinctive reasoning fingerprint. Structural operator features predict within-problem answer correctness well above baselines. Classifiers built on these operators reach WP-AUC and on AIME specifically. ReasonOps further enables early quality estimation well before the trace completes: we predict at WP-AUC for only 50% of the trace. The ReasonOps pipeline is unsupervised and annotation-free, enabling deep insights into LLM reasoning traces as well as strong downstream results on model identification and correctness prediction.
Large language models (LLMs) achieve impressive scores on standard benchmarks yet routinely fail questions that any human would answer correctly in seconds. We introduce BrainBench, a benchmark of 100 brainteaser questions spanning 20 carefully designed categories, each targeting a specific commonsense reasoning failure mode in LLMs. Categories range from implicit physical constraints ("Should I walk or drive my rental car to the return lot?") to semantic scope tricks and default assumption hijacks. We evaluate eight frontier models -- four from the Claude family and four from the GPT family -- using a zero-shot protocol with 10 independent runs per question. The best model, Claude Opus 4.6 with extended thinking, achieves only 80.3% accuracy; the worst, GPT-4o, scores 39.7%. Even top-performing models exhibit a 6-16 percentage-point gap between accuracy and consistency, revealing stochastic reasoning. Cross-lingual evaluation in Chinese shows most models degrade by 2-8 percentage points, confirming that these failures reflect reasoning deficits rather than language-specific artifacts. BrainBench provides a fine-grained diagnostic tool for identifying where and why LLMs substitute surface heuristics for genuine commonsense reasoning.
A standard recipe for distilling the reasoning ability of large language models (LLMs) is to sample chains of thought from the model, keep those that reach the correct final answer, and fine-tune on the survivors. When sampling fails, a common fix shows the generator the gold answer and asks it to write a chain that reaches that answer. We show that this second step degrades the training data in a way that correctness filtering cannot catch. We run a controlled experiment that fixes the generator, the problem set, and the correctness filter, and varies only whether the chain is generated under answer-conditioning, the gold answer shown with a request to reach it. Training a strong instruction-tuned reasoning model on its own answer-conditioned chains sharply lowers its verifiable-reasoning accuracy. The loss grows with difficulty, reaching as much as about 27 points on the hardest competition problems. The mechanism is legible in the chains themselves, which rationalize backward from the shown answer instead of deriving it, with the early final-answer statement as the measurable symptom. The harm is a property of the data rather than the generator, read off unlabeled generations before any fine-tuning, ordering the penalty across eight thinking models from four families, and transferring across teacher families. A prompt ablation localizes it to the rationalize-toward instruction rather than the answer's bare visibility. The practical takeaway is to generate answer-blind, because no correctness filter can see this damage in the data.
Jungseob Lee, Seungyoon Lee, Suhyune Son +4
1Korea University · 2Zoom Communications · 3Yonsei University